Hi David,
The student role can NOT delete other users' entry, this comes as default. If you encountered a strange behaviour, please double check 1. Site level role setting, 2. Category level role override and 3. course level role override
There is No setting/role override to stop a user to delete their own entry.
The setting: mod/data:manage entries can be used to stop a Teacher to delete an entry, or to allow students to delete others' entry.
If you don't want any one to delete any entry, neither their own nor others, simply remove the tag ##delete## from both Single template and List template. When you do want to delete an entry, you can quickly add the ##delete## tag back for a short period during a quiet time. You can also temporarly hide this activity until you have finished your clean up task.